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Simplifying 4x2 + -6x = 3x2 + 6x + -5 Reorder the terms: -6x + 4x2 = 3x2 + 6x + -5 Reorder the terms: -6x + 4x2 = -5 + 6x + 3x2 Solving -6x + 4x2 = -5 + 6x + 3x2 Solving for variable 'x'. Reorder the terms: 5 + -6x + -6x + 4x2 + -3x2 = -5 + 6x + 3x2 + 5 + -6x + -3x2 Combine like terms: -6x + -6x = -12x 5 + -12x + 4x2 + -3x2 = -5 + 6x + 3x2 + 5 + -6x + -3x2 Combine like terms: 4x2 + -3x2 = 1x2 5 + -12x + 1x2 = -5 + 6x + 3x2 + 5 + -6x + -3x2 Reorder the terms: 5 + -12x + 1x2 = -5 + 5 + 6x + -6x + 3x2 + -3x2 Combine like terms: -5 + 5 = 0 5 + -12x + 1x2 = 0 + 6x + -6x + 3x2 + -3x2 5 + -12x + 1x2 = 6x + -6x + 3x2 + -3x2 Combine like terms: 6x + -6x = 0 5 + -12x + 1x2 = 0 + 3x2 + -3x2 5 + -12x + 1x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 5 + -12x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -12x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -12x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -12x + x2 = 0 + -5 -12x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -12x + x2 = -5 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = -5 + 36 Reorder the terms: 36 + -12x + x2 = -5 + 36 Combine like terms: -5 + 36 = 31 36 + -12x + x2 = 31 Factor a perfect square on the left side: (x + -6)(x + -6) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (x + -6) equal to 5.567764363 and -5.567764363.Subproblem 1
x + -6 = 5.567764363 Simplifying x + -6 = 5.567764363 Reorder the terms: -6 + x = 5.567764363 Solving -6 + x = 5.567764363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 5.567764363 + 6 Combine like terms: -6 + 6 = 0 0 + x = 5.567764363 + 6 x = 5.567764363 + 6 Combine like terms: 5.567764363 + 6 = 11.567764363 x = 11.567764363 Simplifying x = 11.567764363Subproblem 2
x + -6 = -5.567764363 Simplifying x + -6 = -5.567764363 Reorder the terms: -6 + x = -5.567764363 Solving -6 + x = -5.567764363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -5.567764363 + 6 Combine like terms: -6 + 6 = 0 0 + x = -5.567764363 + 6 x = -5.567764363 + 6 Combine like terms: -5.567764363 + 6 = 0.432235637 x = 0.432235637 Simplifying x = 0.432235637Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.567764363, 0.432235637}
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